/*
 *   
 *
 * Copyright  1990-2009 Sun Microsystems, Inc. All Rights Reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER
 * 
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License version
 * 2 only, as published by the Free Software Foundation.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * General Public License version 2 for more details (a copy is
 * included at /legal/license.txt).
 * 
 * You should have received a copy of the GNU General Public License
 * version 2 along with this work; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA
 * 02110-1301 USA
 * 
 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa
 * Clara, CA 95054 or visit www.sun.com if you need additional
 * information or have any questions.
 */

/* __kernel_tan( x, y, k )
 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input k indicates whether tan (if k=1) or
 * -1/tan (if k= -1) is returned.
 *
 * Algorithm
 *  1. Since tan(-x) = -tan(x), we need only to consider positive x.
 *  2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
 *  3. tan(x) is approximated by a odd polynomial of degree 27 on
 *     [0,0.67434]
 *                   3             27
 *      tan(x) ~ x + T1*x + ... + T13*x
 *     where
 *
 *          |tan(x)         2     4            26   |     -59.2
 *          |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
 *          |  x                    |
 *
 *     Note: tan(x+y) = tan(x) + tan'(x)*y
 *                ~ tan(x) + (1+x*x)*y
 *     Therefore, for better accuracy in computing tan(x+y), let
 *           3      2      2       2       2
 *      r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
 *     then
 *                  3    2
 *      tan(x+y) = x + (T1*x + (x *(r+y)+y))
 *
 *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
 *      tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
 *             = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
 */

#include "incls/_precompiled.incl"
#include "incls/_Tangent_kernel.cpp.incl"

#if ENABLE_FLOAT

#ifdef __cplusplus
extern "C" {
#endif

static const double
one_t   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
T[] =  {
  3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
  1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
  5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
  2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
  8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
  3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
  1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
  5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
  2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
  7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
  7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
  2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
};

double tangent_kernel(double x, double y, int iy) {
  double z, r, v, w, s;
  int ix, hx;
  hx = __JHI(x);   /* high word of x */
  ix = hx & 0x7fffffff; /* high word of |x| */
  if (ix < 0x3e300000) {           /* x < 2**-28 */
    if (jvm_d2i(x) == 0) {            /* generate inexact */
      if (((ix | __JLO(x)) | (iy + 1)) == 0) {
        return jvm_ddiv(one_t, jvm_fplib_fabs(x));
      } else {
        return (iy == 1)? x: jvm_ddiv(jvm_dneg(one_t), x);
      }
    }
  }
  if (ix >= 0x3FE59428) {            /* |x|>=0.6744 */
    if (hx < 0) {
      x = jvm_dneg(x);
      y = jvm_dneg(y);
    }
    z = jvm_dsub(pio4, x);
    w = jvm_dsub(pio4lo, y);
    x = jvm_dadd(z, w);
    y = 0.0;
  }
  z =  jvm_dmul(x, x);
  w =  jvm_dmul(z, z);
  /* Break x^5*(T[1]+x^2*T[2]+...) into
   *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
   *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
   */
  //r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
  r = jvm_dadd(T[1], jvm_dmul(w, jvm_dadd(T[3], jvm_dmul(w, jvm_dadd(T[5], jvm_dmul(w, jvm_dadd(T[7], jvm_dmul(w, jvm_dadd(T[9], jvm_dmul(w, T[11]))))))))));
  //v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
  v = jvm_dmul(z, jvm_dadd(T[2], jvm_dmul(w, jvm_dadd(T[4], jvm_dmul(w, jvm_dadd(T[6], jvm_dmul(w, jvm_dadd(T[8], jvm_dmul(w, jvm_dadd(T[10], jvm_dmul(w, T[12])))))))))));
  s = jvm_dmul(z, x);
  r = jvm_dadd(y, jvm_dmul(z, jvm_dmul(s, jvm_dadd(jvm_dadd(r, v), y))));
  r = jvm_dadd(r, jvm_dmul(T[0], s));
  w = jvm_dadd(x, r);
  if(ix >= 0x3FE59428) {
    v = jvm_i2d(iy);
    return jvm_dmul(jvm_i2d((1 - ((hx >> 30) & 2))),
     jvm_dsub(v, jvm_dmul(2.0, jvm_dsub(x, jvm_dsub(jvm_dmul(w, jvm_ddiv( w, jvm_dadd(w, v))), r)))));
  }
  if (iy == 1) {
    return w;
  } else {
    /* if allow error up to 2 ulp, simply return -1.0/(x+r) here */
   /*  compute -1.0/(x+r) accurately */
    double a,t;
    z = w;
    __JLO(z) = 0;
    v = jvm_dsub(r, jvm_dsub(z, x));     /* z+v = r+x */
    t = a  = jvm_ddiv(-1.0, w);    /* a = -1.0/w */
    __JLO(t) = 0;
    s = jvm_dadd(1.0, jvm_dmul(t, z));
    return jvm_dadd(t, jvm_dmul(a, jvm_dadd(s, jvm_dmul(t,v))));
  }
}

#ifdef __cplusplus
}
#endif

#endif // ENABLE_FLOAT
